Testing expressibility is hard

Authors:
Ross Willard
Affiliations:
Pure Mathematics Department, University of Waterloo, Waterloo, Ontario, Canada
Venue:
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Year:
2010

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Abstract

We study the expressibility problem: given a finite constraint language Γ on a finite domain and another relation R, can Γ express R? We prove, by an explicit family of examples, that the standard witnesses to expressibility and inexpressibility (gadgets/formulas/conjunctive queries and polymorphisms respectively) may be required to be exponentially larger than the instances. We also show that the full expressibility problem is co-NEXPTIME-hard. Our proofs hinge on a novel interpretation of a tiling problem into the expressibility problem.